緩長記憶與狀態變換

Long Memory and Regime Switch

10.6277/ter.2004.322.2

謝俊魁(Jiun-Kuei Hsieh)；林建甫(Jeff Chien-Fu Lin)

FIGARCH模型 ； Markov-Switching模型 ； SWARCH模型 ； SW(k)-FIGARCH-L模型 ； 緩長記憶 ； FIGARCH model ； markov-switching model ； SWARCH model ； SW(k)-FIGARCH-L model ； long memory

經濟論文叢刊

32卷2期（2004 / 06 / 01）

193 - 232

繁體中文

針對衆所周知之財務資料波動程度的高度相關性，辨別這種相關性是否就是「緩長記憶」在經濟政策、財務決策、實證方法、及計量理論上都具有非常重要的意義。本文結合Hamilton and Susmel (1994)之狀態變換(regime switching)SWARCH模型，以及Baillie，Bollerslev，and Mikkelsen (1996)的緩長記憶FWARCH模型，新創相當一般化之SW(k)-FIGARCH-L (0,d,0)模型，同時估計狀態轉變參數及部分差分係數，使我們既可在狀態變換的前提下檢定緩長記憶假說，也能在考慮緩長記憶可能存在的前提下檢定是否有狀態變換發生，並證明波動程度之狀態變換的確會造成相當嚴重的假性緩長記憶問題。此新模型不但可避免以單純緩長記憶模型估計狀態變換母體所導致的假性緩長記憶問題，更解決了單純狀態變換模型殘差項平方值仍具高度跨期相關的窘境，是一個相對優良的模型，在財務資料的估計上十分具有發展潛力。根據實證結果，未考慮狀態變換因素前，台股指數日報酬率的波動程度的確顯現出緩長記憶特徵，然而同時考慮狀態變換因素後，緩長記憶特徵不復存在，僅具中等記憶。

The strong persistence in volatility of a variety of financial time series is well known. To determine whether this persistence can be characterized as ”long memory” is important in both financial and econometric modelling. In this pa per, after summarizing Hamilton and Susmel's (1994) regime switching SWARCH model and BBM's (1996) long memory FIGARCH for volatility; we propose a general SW(k)-FIGARCH-L(0,d,0) model that allows the estimation of both regime switching parameters and the long memory parameter. In such a frame work we are able to test whether the volatility still has long memory after regime switching has been considered and we show that regime switching in volatility can result in spurious long memory. Furthermore, we find the proposed model also solves one of the problems with the standard SWARCH model that squared residuals obtained from the SWARCH model estimation usually are highly correlated, which implies the simple regime switching mechanism is not able to characterize all the dynamics in volatility. Based on these encouraging results, we believe the proposed model is a promising tool in analyzing financial data. Our empirical analysis of the TAIEX data shows that the long memory in their volatility will reduce to intermediate memory after regime switching is considered, which represents an interesting example of spurious long memory in volatility that is caused by the regime switching.

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